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The Computer Journal Advance Access published online on March 31, 2008
The Computer Journal, doi:10.1093/comjnl/bxn004
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© The Author 2008. Published by Oxford University Press on behalf of The British Computer Society. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Synchronized Interactions in Spiked Neuronal Networks

Erol Gelenbe* and Stelios Timotheou

Intelligent Systems and Networks Group, Department of Electrical and Electronic Engineering, Imperial College, London SW7 2BT, UK

* Corresponding author: e.gelenbe{at}imperial.ac.uk

Received 21 December 2007; The study of artificial neural networks has originally been inspired by neurophysiology and cognitive science. It has resulted in a rich and diverse methodology and in numerous applications to machine intelligence, computer vision, pattern recognition and other applications. The random neural network (RNN) is a probabilistic model which was inspired by the spiking behaviour of neurons, and which has an elegant mathematical treatment that provides both its steady-state behaviour and offers efficient learning algorithms for recurrent networks. Second-order interactions, where more than one neuron jointly act upon other cells, have been observed in nature; they generalize the binary (excitatory–inhibitory) interaction between pairs of cells and give rise to synchronous firing (SF) by many cells. In this paper, we develop an extension of the RNN to the case of synchronous interactions, which are based on two cells that jointly excite a third cell; this local behaviour is in fact sufficient to create SF by large ensembles of cells. We describe the system state and derive its stationary solution as well as a O(N3) gradient descent learning algorithm for a recurrent network with N cells when both standard excitatory–inhibitory interactions, as well as SF, are present.

Key Words: random neural network • synchronized interactions • learning algorithm


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